Multiply the following complex numbers: $({2+5i}) \cdot ({-3-i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2+5i}) \cdot ({-3-i}) = $ $ ({2} \cdot {-3}) + ({2} \cdot {-1}i) + ({5}i \cdot {-3}) + ({5}i \cdot {-1}i) $ Then simplify the terms: $ (-6) + (-2i) + (-15i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (-2 - 15)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -6 + (-2 - 15)i - (-5) $ The result is simplified: $ (-6 + 5) + (-17i) = -1-17i $